How to play Kakurasu

Shade squares so each row and column adds up to its total — a shaded square is worth its column number in its row and its row number in its column. Also known as Index Sums, Weighted Sums.

▶ Play Kakurasu ⊞ Open the solver

The rules

The columns are numbered 1, 2, 3… from the left, and the rows 1, 2, 3… from the top.
A shaded square adds its column number to its row’s total, and its row number to its column’s total.
Every row must add up to the number on its right, and every column to the number underneath.
Unshaded squares add nothing.

Playing Kakurasu on Puzzle Solvers

Choose a size and a difficulty, then press New Puzzle.
Tap a square to shade it, tap again to mark it empty. Drag to do several. Shaded squares show their value.
Your running totals show beside each row and under each column, and turn green when they match.
Hint lists the sets that can make a total and shades what they all agree on.

Open the Kakurasu game →

Using the Kakurasu solver

Choose the size, then click each total and type it (or press Sample).
Press Solve and step through: for each row or column, the sets of numbers that make its total, and what they all agree on.

Open the solver →

A worked example

In a 5×5 puzzle, column 2 has a total of 2. Only row 2 is worth 2 on its own, so in column 2 just the square in row 2 is shaded.

Row 2 must make 5: with column 2 already shaded (worth 2), it needs 3 more — that is column 3 alone, or columns 1 and 2, but 2 is used. So column 3 is shaded and the rest of row 2 is empty.

Strategies

Tiny and huge totals. A total of 1 or 2 has only one way to be made. A total of 1+2+…+N shades the whole line; one less than that leaves out only square 1.
List the sets. Write the ways to make a total: in a 6-wide row, 7 is 1+6, 2+5, 3+4, 1+2+4. Squares in every set are shaded; squares in none are empty.
Cross-check. A column that cannot use row 3 rules out every set for row 3 that uses that column.
Count from the top. The total of all row totals equals the total of all column totals’ partners — use it to check your copy.
Work the extremes. Start with the smallest and largest totals; they have the fewest sets.

Common mistakes

Using a square’s row number in its row — in a row, a square is worth its column number.
Forgetting that the same number cannot be used twice in one line.
Shading to fix a row without checking the columns that cross it.

Where it comes from

Kakurasu (from Japanese for ‘hide’) is a modern Japanese pencil puzzle that became popular in puzzle apps as a quick sums puzzle.

Frequently asked questions

What are the small numbers outside the grid?

Across the top: what a shaded square is worth in its row. Down the left: what it is worth in its column. Totals are on the right and at the bottom.

What maths does it practise?

Adding small numbers and finding all the ways to make a total — the same skill as number bonds and partitions.

Is there always one answer?

Yes — every puzzle here is checked to have exactly one solution.

How do I solve one from a book?

Open the Kakurasu Solver, type the totals and press Solve.

Keep going

All guides: How to play every puzzle and game.